How many square units are in the area of the triangle whose vertices are the $x$ and $y$ intercepts of the curve $y = (x-3)^2 (x+2)$?
First, we need to find where this curve intersects the $x$ and $y$ axes.  If $y=0$, then $(x-3)^2(x+2)=0$, which has solutions of $x=3$ and $x=-2$.  If $x=0$, then $y=(-3)^2(2)=18$.  So, the curve has two $x$-intercepts and one $y$-intercept.  The length of the base along the $x$-axis is $3-(-2)=5$.  The height from this base is equal to the $y$-intercept, 18.  The area of the triangle is $\frac{1}{2}\cdot 5\cdot 18=\boxed{45}$.